(Solved): 2) The elementary gas-phase reaction \[ \left(\mathrm{CH}_{3}\right)_{3} \mathrm{COOC}\left(\mathr ...

2) The elementary gas-phase reaction \[ \left(\mathrm{CH}_{3}\right)_{3} \mathrm{COOC}\left(\mathrm{CH}_{3}\right)_{3} \rightarrow \mathrm{C}_{2} \mathrm{H}_{6}+2 \mathrm{CH}_{3} \mathrm{COCH}_{3} \] is carried out isothermally in a flow reactor with no pressure drop. The specific reaction rate at \( 50^{\circ} \mathrm{C} \) is \( 10^{-4} \mathrm{~min}^{-1} \) and the activation energy is \( 85 \mathrm{~kJ} / \mathrm{mol} \). Pure di-tert-butyl peroxide enters the reactor at 10 atm and \( 127^{\circ} \mathrm{C} \) and a molar flow rate of \( 2.5 \mathrm{~mol} / \mathrm{min} \). Calculate volume and space time to achieve \( 90 \% \) conversion in: (a) a CSTR (b) a PFR (c) If this reaction is to be carried out at \( 10 \mathrm{~atm} \) and \( 127^{\circ} \mathrm{C} \) in a batch mode with \( 90 \% \) conversion, what reactor size that would be required to process \( (2.5 \mathrm{~mol} / \mathrm{min} * 60 \mathrm{~min} / \mathrm{h} * 24 \mathrm{~h} / \) day \( ) 3600 \mathrm{~mol} \) of di-tert-butyl peroxide per day? (d) Assume that the reaction is reversible with \( \mathrm{KC}=0.025 \mathrm{~mol}^{2} / \mathrm{dm}^{6} \) and calculate the equilibrium conversion and then redo (a) through (c) to achieve a conversion that is \( 90 \% \) of the equilibrium conversion. (Hint: Remember that the equilibrium conversion will be different for a flow reactor and a constantvolume batch reactor for a gas-phase reaction that has a change in the total number of moles).